and electrical properties of full-size ITER conductor samples under transverse ... section of 400 mm length at 4.2 K. The jacket is partly opened in order to transmit the ..... of 1.5 when a load is applied, while the intra-petal R, decreases -1.5 ...
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 9, NO. 2, JUNE 1999
1069
Electromagnetic and Mechanical Characterisation of ITER CS-MC Conductors Affected by Transverse Cyclic Loading, Part 1: Coupling Current Loss Arend Nijhuis, Niels H.W. Noordman and Herman H. J. ten Kate University of Twente, Faculty of Applied Physics, P.0. Box 217, 7500 AE Enschede, The Netherlands Neil Mitchell ITER JCT 80 1- 1 Mukouyama, Naka-machi, Naka-gun, Ibaraki-ken 3 11-01, Japan. Pierluigi Bruzzone EPFL-CUP, PSI, Villingen, CH 5232, Switzerland Abstract- The magnetic field generated by a coil acts on the cable which results in a transverse force on the strands. This affects the interstrand contact resistances (RJ, the coupling current loss and current redistribution during field changes. A special cryogenic press has been built to study the mechanical and electrical properties of full-size ITER conductor samples under transverse, mechanical loading. The cryogenic press can transmit a variable (cyclic) force up to 650 kN/m to a conductor section of 400 mm length at 4.2 K. The jacket is partly opened in order to transmit the force directly onto the cable. In addition a superconducting dipole coil provides the magnetic field required to perform magnetisation measurements using pick-up coils. The various R,’s between strands selected from different positions inside the cable have been studied. The coupling loss time constants (nzj during and after loading are verified for the Nb,Sn, 45 kA, 10 and 13 T, ITER Model Coil conductors. A summary of the results obtained with up to several tens of full loading cycles is presented. A significantdecrease of the cable n I after several cycles is observed. The values of the n.r ‘s are discussed with respect to the R, measurements and a multiple time constant model (MTC).
I. INTRODUCTION Heavy transverse loading of the ITER conductors [I] due to Lorentz forces in the coils is the cause of mechanical effects and variations in the transverse electrical resistivity and contact patterns in the cable. A distinction can be made between electromagnetic and mechanical AC losses in a conductor. The mechanical AC loss is mainly caused by friction and deformation and is indirectly originated by the Lorentz forces on the conductor [2]. The electromagnetic loss is caused by a change of transport current or applied magnetic field. The electromagnetic AC losses in superconductors without transport current but with an applied alternating external field consist of hysteresis and coupling loss [3]. When the conductor carries a transport current, the enhanced interstrand conductivity due to the Lorentz force working on the contacts in a cable is a potential reason for higher coupling loss. An important parameter that determines the coupling currents between strands in superconducting cables is the inter-strand resistance. Its value depends on a variety of factors, such as the cable layout, internal strand Manuscript received September 14, 1998. These investigations are part of the NET contract No. 95/389 between the EU and the University of Twente A. Niihuis, +31.53.489.3889, fax +3 1.53.489.1099, a.niihuis@,h.utwente.nl
1051-8223/99$10.00
geometry, compacting factor, production conditions, impregnation, temperature, transverse load, strand surface properties, contact deformation and history [4]-[7]. Previous work thoroughly addressed experimentally the dependence of the cable coupling loss on cabling parameters such as void fraction, strand surface Cr layer thickness and vendor, type of cabling and cabling stage [4],[5]. In experiments with transport current in sub-size cables it is observed that n zat zero current declines during cyclic loading, from a substantially higher value in the virgin state to approximately 2 ms after several cycles [6]. Also the influence of cyclic bending on sub-size CIC specimen up to a strain level of 0.4 % has caused n z to drop to 2 ms [7]. These effects can explain the big difference found between the high n r-values of samples in the virgin state and the low n z‘s as for example in the DPC magnets [8] and decreasing n z of the ENEA coil with cyclic loading [9]. It is also found that the transverse Lorentz force acting on strands may reduce the R, between strands in the cable and as a consequence, the n Twill increase [7]. The geometry, the Lorentz force and the manufacturing conditions determine the interstrand coupling loss. The influence of a transverse (cyclic) force on the AC loss of fullsize ITER conductors has not yet been studied in any detail. Therefore a special cryogenic press was built. The aim of this study is to measure the mechanical (deformation, elastic module, frictional heating) and electrical (transverse interstrand and -stage R, and nzj properties of full-size cable samples under transverse, mechanical loading. Moreover, force-displacement measurements provide information on effective Young’s modulus (E) and frictional heating effects. The Re's and mechanical properties are presented in [2],[10] and the results. Some characteristic parameters of the multistage cables are gathered in Table I [ 11. TABLEI. SOME CHARACTERISTIC PROPERTIES OF THE ITER CONDUCTORS.
cs1.1 Strand diameter [mm] No. sup. cond. strands No. of Cu strands Twist pitches [mm] Cable pattern Cable diameter [mm] Local void fraction
0 1999 IEEE
cs2
0.81 0.81 1152 720 0 360 25x 5 4 x 9 5 ~ 1 4 7 ~ 3 9 75 0 ~ 1 0 4 ~ 1 5 2 ~ 2 5 9 ~ 3 9 4 3x4~4~4~6 3x3~4~5~6 40.9 37.5 36 Yo 36 Yo
1070
11. AC LOSSES
The coupling loss can be represented by the energy loss per cycle versus frequency, assuming that the hysteresis loss per cycle at low excitation i.e. full penetration of the applied field, is independent of the frequency 0 : n-.B: . W .n z Qcpi = [J/m3.cycle]. (1) PQ
The applied field is Basin(2$ii and n is the shape factor [3]. The fraction of the strand volume involved in the loss creation is supposed to be included in n. In fact n stands for a geometry factor which also represents the. fraction of superconductor. The time constant I [SI is the decay time constant of the induced currents. For monolithic conductors the time constant can be written as:
where Lp is the twist pitch (or the characteristic length of a coupling current path) and p1 is the effective electrical resistivity in the transverse direction. The slope a of the linear section of the loss curve, Q,u>, at low frequency provides the effective coupling current tune constant n zas described before: (3) The n z value can be used for AC loss calculations of magnets operating at low ramp rates. Then the hysteresis loss is taken to be independent of frequency. At higher ramp rates the coupling loss saturates and subsequently decreases with frequency due to shielding of the interior of the conductor. When only one dominant coupling loss time constant is present, then the coupling loss over an extended frequency range is given by [3]: n.B: . W .n z [J/m3.cycle]. (4) Q,i = .(1+ w’z’) In the case of multistage cables, many different current loops are created by strand-to-strand crossover contacts everywhere in the cable. In the case of a regular cable pattern some loops with similar properties will occur more often than others and may even result in dominant decay time constants. Depending on the cabling geometry, it is possible that higher cable stages have a large number of coupling current paths due to many strand contacts with a large spread in contact resistances and coupling current loops with a current path even far exceeding the cabling pitch of the last stage [12]. The actual contact resistances strongly depend on the crossing angle, coatings, pressure and history [4]-[7]. In multistage cables, this may lead to a large number of time constants even without any dominant time constant(s). In fact, it means the loss represented by a particular time constant is created in only a (small) part of the total cable volume and a various spectrum of time constants exists. A part of the different loops will be strongly shielded and others hardly.
In the case of a strand, the volume fraction is approximately the volume of the closely pack1:d multifilamentary zone scaled to the total strand volume [:!I. For inter-strand coupling loss the volume involved in a coupling current path is not known with any reasonatile precision and is generally different for each time constant in the cable. In the general case with multistage cables, a large number of different coupling current loops exist, each linking a different volume fraction of cable and with different time constants. These volume fractions may be very small in relation to the total cable volume but can be spread out along a relatively long cable length. As a consequence, the coupling loss over an extended range of frequencies can not be described with (4) using a single time constant of the cable as a system. For that reason, (4) is extended to a new, but simplified model, assuming the presence of N dominant time constants all interacting by shielding with a weighted volume fraction included in n expressed by: (5):
The shape factor nk includes the volume fraction involved in the creation of coupling current loss represented by the time constant zk.. Note that (5) still implies that the effective n z value from (3) determined by the low frequency limit can be regarded as the summation of the contributions 2 n k ’ f k , for all time constants. n z = C n k z k, Relation (5) can be used to fit N effective time constants, to the measured coupling loss curve. However, the accuracy of a set of time constants obtained from a fit of Relation 5 to a measured loss versus frequency curve Q,,,@ highly depends on the range of frequency in relation to the time constants present in a cable. Beside that the choice of N, the accuracy of the measured data, and the frequency interval also play a role. If these conditions are prosperous then the proposed simplified model can be useful for analyses of data. The interaction between current paths can be disregarded when frequency (or dB/dt) is low and the shielding effect is not relevant. However, in many cases the deviation fiom linearity already appears at a relatively very low frequency. Therefore this effect should be considered in AC loss experiments on multi-strand and -stage conductors. In order to determine a reliable initial slope the frequency should be low compared to the expected highest time constants. In the presence of relatively high hysteresis loss it is necessary to consider the shielding effect on the hysteresis loss at higher frequencies. The frequency dependent model for sinusoidal applied fields can be expressed as [13]: nk.2,
in which: Q,,,,,=hysteresis loss [J/m3], Q,,=hysteresis loss at
PO Hz [Urn3]and B,=penetration field [TI [3].
In the case of multistage cables we can transform the above relations into:
1071 N
12
k=l
Some parts of the cable may possibly become saturated with current as dB/dt increases and if the total current exceeds the in particular in the strands involved in critical value (ZX,), the loops with the hghest time constants. The above relations do not take into account saturation which would prevent stronger shielding with an increasing dBJdt. Also complicated demagnetisation effects caused by shape factors and current distributions are not implemented in the model. The MTC model has been tested on a limited scale with single triplet twisted cables [14]. In these experiments the model appeared to be very useful for the analyses of the measured AC loss data regarding the present time constants in relation to the varied pitches and R,’s. The MTC model as discussed above is only applicable to sinusoidal sweeps and is further used for the interpretation of the results. I11 MAGNETISATION MEASUREMENT RESULTS Two conductors CS1, (high field) and CS2 (medium field) were taken from the prototype CSMC production [ 11, layers 1.1 and 2. The details of the cryogenic press, the sample preparation and its instrumentation are reported in [15]. The magnetisation measurements were carried out using compensated pick-up coils. Figure 1 shows the total loss versus the frequency of the applied sinusoidal field for the CS 1.1 specimen in the virgin state and after 38 loading cycles from zero to 650 kN/m [2] with and without load. The data can be used to fit a set of time constants using the MTC model. If the majority of the z’s are relatively small regarding the maximum measured frequency then it is not useful to chose N>2 because the model is not able to make a clear distinction between the smaller z’s within a very limited frequency range. The values for z, and nk found after fitting are gathered in Table 11. The values found for n zusing the initial slope of the loss curve are presented in the right column of Table 11. The n zof the virgin cable for Ba=200 mT in 0.6 T DC background field amounts to 143 111s. The nzdetermined from the initial O Hz with the MTC model decreases with the slope at P number of cycles to 33 ms after 38 cycles in the case without load (F=O kN). If a load is applied of 650 kN/m, then the n z increases to 74 ms. It should be emphasised here that these nz’s are estimated using the initial slope of the loss versusf curve. These values are not applicable for a calculation of the coupling loss at higher frequencies because they will clearly result into an over estimation of the loss. A distinction can be made between the coupling loss at very low and higher regimes of the field ramp rate. The n ztaken from the slope of the loss curve for a cycle time T=l&30 s is 30 ms with full load and 2 1 ms without load. It is striking that the MTC analyses gives a very high time constant of 4 s for a loaded cable in apparently a very small volume fraction. It contributes for more than an equivalent part (n,q=41 ms) to the total coupling loss in comparison
1
I
for Ba>Bp. ( 8 ) Q,,,,, = Q,, . n ( l + nku2zk2)-0.5
I
Measured and calculated
10
2
I0
-Qcalc,
Qmeas,virgin
I
virgin
0
0
0.04
0.02
0.06
0.1
0.08
frequency [Hz]
Figure 1. Results of the magnetisation measurements with pick-up coils on the CSI.1B sample and calculation of the loss in the virgin state and after 38 full loading cycles with and without load. B,=200 mT and the Bd,=0.6 T.
TABLE11. ZAND n-VAL.UES (CSI) FOUND AFTER FITTING THE MEASURED MAGNETISATION DATA TO THE MTC MODEL AND TO THE INITIAL SLOPE.
Condition Virgin
0 kN/m and 38 cycles 650kN/mand 38 cycles
k 1 2 1
2 1 2
%
nk%
I-1
rmsl
lmsl
Imsl
0.25 0.09 0.077 0.012 0.010 1.36
510 140 380 273 3930 24
130 12.5 29 3.2 41 33
143
‘k
Cnkz,
33
74
to the lower time constant (n,z,=33 ms). It is assumed that the hysteresis loss is identical in both cases with and without load. This is not necessarily correct because the critical current and thus the hysteresis loss depends on the strain and thus on the applied pressure (F).The penetration field B, for the CS1.l conductor for low f and B,,=0.6 T is 80 mT. Considering Ba=200 mT this influence can be disregarded. The values found by the MTC model agree very well with the results obtained with the R, measurements [lo]. The coupling loss for a time period T
